Solving for temperature and volume of Dietrici Equation

[Riverbirdy]

Hi, guys! I came across hard stuff today. I really hope you can help a poor little worm like me. How do you solve for v & T correspondingly for equation like this⇒p = [RT/(v-b)]e^(a/vRT)?
What's the technique? How do you call it?

 

[Charles Link]

The exponential can be expanded (Taylor series) $e^x=1+x +x^2/2+... =1+x$ for small $x$ . Normally, iterative techniques work well in solving this type of equation. To first order $v=RT/p$, etc. You take this $v$ and write out the solution for $v$ on the left with higher order terms on the right side of the equation. Then you get an improved answer for $v$ and cycle it around again, etc. Also $v-b=v(1-b/v)$ etc. The $1/(1-b/v)$ can stay on the right side and bring the $v$ to the left...You can even write $1/(1-b/v)=1+(b/v)+(b/v)^2+(b/v)^3+...$. (i.e. a geometric series $1+r+r^2+r^3+...=1/(1-r))$.